Liquidity & price impact

When can a higher-fee pool give a better execution price?

Compare a lower-fee shallow pool with a higher-fee deeper pool by calculating output at the same input size.

A higher pool fee can be outweighed by better depth at the requested size. Compare final quoted output after the pool charge; the advertised fee rate alone does not determine which pool gives the better exchange.

A controlled hypothetical example

Take two equal-price constant-product pools with one-for-one starting reserve ratios. Shallow Pool A holds 10,000 tokens per side and charges a hypothetical 0.10%. Deep Pool B holds 100,000 per side and charges 0.30%.

For 1,000 input tokens, A's effective input is 999 and modeled output is about 908.264388. B's effective input is 997 and output is about 987.158034. B delivers substantially more despite the larger fee rate.

The ranking can change at small sizes

For a sufficiently small trade, both pools have little size effect and the lower fee can become more significant. That is why the comparison must use the intended amount rather than a provider's lowest published fee.

The reference constant-product calculation combines an effective input with reserve-dependent output. The fee rates and reserves here are illustrative model inputs, not current provider prices.

Finish the economic comparison

Add separate network and preparation costs after comparing received tokens. If accessing B requires enough extra gas, a modest output advantage at a smaller size can disappear. A large raw-output advantage and a tiny one should not be treated alike.

Also match initial prices and token identities. A better starting price can independently affect the quote. Concentrated pools require their range distribution rather than this two-reserve shortcut.

The useful question is not whether a fee tier is low, but whether the particular quote delivers better net value for the actual trade. Retain the fee rate as one explanatory component of that result.

Sources & verification (1)

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  1. UniswapV2Library.sol

    Reference amount-out and amount-in arithmetic; integer rounding.

    https://github.com/Uniswap/v2-periphery/blob/master/contracts/libraries/UniswapV2Library.sol

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